Alternative proof of Mulholland’s theorem and new solutions to Mulholland inequality

Authors: Milan Petrík, M. Navara, P. Sarkoci
Publication year: 2013
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: ISMVL 2013. IEEE 43rd International Symposium on Multiple-Valued Logic
Projects: Mathematical Fuzzy Logic in Computer Science
Bibliographic citation: PETRÍK, Milan, NAVARA, M., SARKOCI, P. Alternative proof of Mulholland’s theorem and new solutions to Mulholland inequality. In: ISMVL 2013. IEEE 43rd International Symposium on Multiple-Valued Logic. Los Alamitos: IEEE Computer Society, 2013, S. 346-351. ISBN 978-0-7695-4976-7. ISSN 0195-623X
Dostupné z: doi:10.1109/ISMVL.2013.1
DOI: 10.1109/ISMVL.2013.1
ID: 395238

Abstract

Mulholland inequality is a real functional inequality presented in 1950 in a paper by Mulholland as a generalization of the Minkowski inequality. In his paper, Mulholland has also provided a sufficient condition for the inequality to be satisfied. However, until now, it has remained an open problem whether this sufficient condition is also necessary. This paper investigates a geometric interpretation of Mulholland inequality and offers a class of functions satisfying the inequality which is strictly larger compared to the class delimited by the Mulholland’s condition. Thus, it is proven that the condition is not necessary.